Gaussian states minimize the output entropy of one-mode quantum Gaussian channels

Abstract

We prove the longstanding conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the Entropy Power Inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p->q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

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• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Limits on classical communication from quantum entropy power inequalities
• Information trade-offs for optical quantum communication
• The classical capacity of quantum thermal noise channels to within 1.45 bits
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• Capacities of Quantum Amplifier Channels
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels
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• Gaussian Thermal Operations and the Limits of Algorithmic Cooling
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• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Gaussian optimizers for entropic inequalities in quantum information
• Approximate reversal of quantum Gaussian dynamics
• Capacities of Quantum Amplifier Channels
• The conditional entropy power inequality for quantum additive noise channels
• The Wehrl entropy has Gaussian optimizers
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Norms of quantum Gaussian multi-mode channels
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• The Entropy Power Inequality with quantum conditioning
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Time-local optimal control for parameter estimation in the Gaussian regime
• Conditional quantum entropy power inequality for $d$-level quantum systems
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Computable limits of optical multiple-access communications
• Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels